三角函数值表格及公式
网校导读：三角函数在各个领域都有着广泛的应用，例如导航、工程学以及物理学，其主要用于计算三角形中未知的边长和角度。为了方便大家学习，网校整理了以下三角函数值表格及常用公式，供参考。
一、三角函数公式大全
1. 两角和与差公式
sin(a + b) = sinacosb + cosasinb
sin(a - b) = sinacosb - sinbcosa
cos(a + b) = cosacosb - sinasinb
cos(a - b) = cosacosb + sinasinb
tan(a + b) = (tana + tanb) / (1 - tanatanb)
tan(a - b) = (tana - tanb) / (1 + tanatanb)
cot(a + b) = (cotacotb - 1) / (cotb + cota)
cot(a - b) = (cotacotb + 1) / (cotb - cota)
2. 倍角公式
sin2a = 2sina cosa
cos2a = (cosa)^2 - (sina)^2 = 2(cosa)^2 - 1 = 1 - 2(sina)^2
tan2a = 2tana / [1 - (tana)^2]
3. 半角公式
sin(a/2) = ±√((1 - cosa) / 2)
cos(a/2) = ±√((1 + cosa) / 2)
tan(a/2) = ±√((1 - cosa) / (1 + cosa)) = (1 - cosa) / sina = sina / (1 + cosa)
cot(a/2) = ±√((1 + cosa) / (1 - cosa))
4. 和差化积公式
sina + sinb = 2sin((a + b) / 2)cos((a - b) / 2)
cosa + cosb = 2cos((a + b) / 2)sin((a - b) / 2)
tana + tanb = sin(a + b) / cosacosb
2sinacosb = sin(a + b) + sin(a - b)
2cosasinb = sin(a + b) - sin(a - b)
2cosacosb = cos(a + b) + cos(a - b)
-2sinasinb = cos(a + b) - cos(a - b)
5. 积化和差公式
sin(a)sin(b) = -1/2 [cos(a + b) - cos(a - b)]
cos(a)cos(b) = 1/2 [cos(a + b) + cos(a - b)]
sin(a)cos(b) = 1/2 [sin(a + b) + sin(a - b)]
6. 诱导公式
sin(-a) = -sin(a)
cos(-a) = cos(a)
sin(pi/2 - a) = cos(a) (pi = 3.1415926....)
cos(pi/2 - a) = sin(a)
sin(pi/2 + a) = cos(a)
cos(pi/2 + a) = -sin(a)
sin(pi - a) = sin(a)
cos(pi - a) = -cos(a)
sin(pi + a) = -sin(a)
cos(pi + a) = -cos(a)
7. 万能公式
sin(a) = (2tan(a/2)) / (1 + tan^2(a/2))
cos(a) = (1 - tan^2(a/2)) / (1 + tan^2(a/2))
tan(a) = (2tan(a/2)) / (1 - tan^2(a/2))
tga = tana = sina / cosa
8. 其它公式
a sin(a) + b cos(a) = √(a^2 + b^2)sin(a + c) [其中，tan(c) = b/a]
a sin(a) - b cos(a) = √(a^2 + b^2)cos(a - c) [其中，tan(c) = a/b]
1 + sin(a) = (sin(a/2) + cos(a/2))^2
1 - sin(a) = (sin(a/2) - cos(a/2))^2